When two parties communicate via a telecommunications network, it is common for the parties:                i. to encrypt their messages so that they remain secret from eavesdroppers, and        ii. to authenticate the messages so that the receiver is confident who really sent the message.It is well known in the prior art how to encrypt and authenticate messages using one or more secure strings of symbols. There are many well-known ways of establishing secure strings, but the process of establishing secure strings in the prior art has disadvantages.        